Physical/mathematical laws describing electrical insulation aging play a key role for the reliability model identification of the insulation itself. This holds for the popular Inverse Power Model, too. The paper first discusses the deduction of the Inverse Power Model from reasonable physical and mathematical models of ageing, described via proper characterization of the random variables or the stochastic processes involved. Then, some analytical aids are given in order to perform its identification and Bayes Estimation, also by means of numerical applications with reference to in-service electrical failure data